QIN Yan-mei, FENG Min-fu, LUO Kun, WU Kai-teng. Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013
Citation: QIN Yan-mei, FENG Min-fu, LUO Kun, WU Kai-teng. Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013

Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations

doi: 10.3879/j.issn.1000-0887.2010.05.013
  • Received Date: 2009-10-26
  • Rev Recd Date: 2010-03-22
  • Publish Date: 2010-05-15
  • The results of Matthies, Skrzypacz and Tubiska for the Oseen problem to the Navier-Stokes problem were extended. For the stationary incompressible Navier-Stokes equations, a local projection stabilized finite element scheme was proposed. The schem eovercomes convection dominated and ameliorates the restrictiveinf-supcondition. Local projection schemes were derived not only as a two-level approach but also for pairs of spaces which were defined on the samemesh. This class of stabilized schemes uses approxmiation and projection spaces defined on the same mesh and leads to much more compact stencils than in the two-level approach. On the same mesh, bes ides the class of local projection stabilization by enrichment of the approximation spaces, two new classes of local projection stabilization of the approximation spaces which dont. need to be enriched by bubble functions are derived. Based on a special in terpolation, the stability and an optimal priorierror estimates were shown. Finally, the numerical tests and the numerical computations show that the numerical results agree with some ben chmark solutions, which further poved the correctness of the theoretical analysis.
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